The arrests come just three weeks before the Summer Olympics.
The arrests, which took place earlier this week, were announced a day after officers in London detained six other terror suspects using stun guns and smoke grenades in early-morning swoops, including one on a home close to London's Olympic Park.
Police said three of the men were arrested Tuesday, three on Wednesday and one on Thursday. Six of them are in their twenties and from the West Midlands, while one is in his 40s and from West Yorkshire. Police said the new arrests were not linked to the London raids.
Police insist that the 13 arrests in recent days did not involve threats to the Olympics set to begin in three weeks. But the counter-terror sweeps have raised anxiety in the run-up to the games.Prime Minister David Cameron's spokesman Steve Field insisted there was no sense of alarm at the spate of arrests so close to the start of the Summer Games.
"We have been looking at the issue of security at the Olympics for some time and we have robust plans in place," he told reporters.
The Associated Press contributed to this report.